Fractional integral estimations pertaining to generalized $ {\gamma} $-convex functions involving Raina's function and applications

Author:

Bin-Mohsin Bandar1,Awan Muhammad Uzair2,Javed Muhammad Zakria2,Kashuri Artion3,Noor Muhammad Aslam4

Affiliation:

1. Department of Mathematics College of Science King Saud University, Riyadh, Saudi Arabia

2. Department of Mathematics, Government College University, Faisalabad, Pakistan

3. Department of Mathematics, Faculty of Technical and Natural Sciences, University "Ismail Qemali", 9400 Vlora, Albania

4. Department of Mathematics, COMSATS University Islamabad, Islamabad, Pakistan

Abstract

<abstract><p>In this paper, we derive a new fractional integral identity and using this identity as an auxiliary result, some new trapezium like inequalities essentially using the class of generalized $ {\gamma} $-convex functions are established. In order to show the efficiency of the obtained results, we discuss and present some special cases and applications.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

Reference45 articles.

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3. E. K. Godunova, V. I. Levin, Neravenstva dlja funkcii sirokogo klassa, soderzascego vypuklye, monotonnye i nekotorye drugie vidy funkii, Vycislitel. Mat. Fiz. Mezvuzov. Sb. Nauc. Trudov, 1985,138–142.

4. S. Varošanec, On $h$-convexity, J. Math. Anal. Appl., 326 (2007), 303–311. https://doi.org/10.1016/j.jmaa.2006.02.086

5. S. Wu, M. U. Awan, M. A. Noor, K. I. Noor, S. Iftikhar, On a new class of convex functions and integral inequalities, J. Inequal. Appl., 2019 (2019), 131. https://doi.org/10.1186/s13660-019-2074-y

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